The field of the invention is nuclear magnetic resonance imaging methods and systems. More particularly, the invention relates to the correction of image artifacts caused by "Maxwell terms" produced by imaging gradients in MRI systems.
When a substance such as human tissue is subjected to a uniform magnetic field (polarizing field B.sub.0), the individual magnetic moments of the spins in the tissue attempt to align with this polarizing field, but precess about it at their characteristic Larmor frequency. If the substance, or tissue, is subjected to a magnetic field (excitation field B.sub.1) which is in the x-y plane and which is near the Larmor frequency, the net aligned moment, M.sub.z, may be rotated, or "tipped", into the x-y plane to produce a net transverse magnetic moment M.sub.t. A signal is emitted by the excited spins, and after the excitation signal B.sub.1 is terminated, this signal may be received and processed to form an image.
When utilizing these signals to produce images, magnetic field gradients (G.sub.x, G.sub.y, and G.sub.z) are employed. Typically, the region to be imaged is scanned by a sequence of measurement cycles in which these gradients vary according to the particular localization method being used. The resulting set of received NMR signals are digitized and processed to reconstruct the image using one of many well known reconstruction techniques.
It is well known that imperfections in the linear magnetic field gradients (G.sub.x, G.sub.y, and G.sub.z) produce artifacts in the reconstructed images. It is a well known problem, for example, that eddy currents produced by gradient pulses will distort the magnetic field and produce image artifacts. Methods for compensating for such eddy current errors are also well known as disclosed, for example, in U.S. Pat. Nos. 4,698,591; 4,950,994; and 5,226,418.
It is also well known that the gradients may not be perfectly uniform over the entire imaging volume, which may lead to image distortion. Methods for compensating this non-uniformity are well known, and for example, are described in U.S. Pat. No. 4,591,789.
Other than uncompensated eddy current errors and gradient non-uniformity errors that escape correction, it can be assumed that the magnetic field gradients (G.sub.x, G.sub.y, and G.sub.z) produce linear magnetic fields exactly as programmed, thus spatially encoding the NMR data accurately. With these gradients, the overall magnetic field at location (x,y,z) is conventionally given as B.sub.0 +G.sub.x x+G.sub.y y+G.sub.z z, and the direction of the field is usually thought to be along the z-axis. This description, however, is not exactly correct. As long as a linear magnetic field gradient is applied, the overall magnetic field is nutated away from the z-axis and its amplitude exhibits higher-order spatial dependencies (x.sup.2, y.sup.2, z.sup.2, x.sup.2 z, . . . ). These phenomena are a direct consequence of the Maxwell equations which require that the overall magnetic field satisfy the following two conditions: .gradient..multidot.B=0 and .gradient..times.B=0 (assuming the true and displacement current densities are zero). The higher-order magnetic fields, referred to as "Maxwell terms" (or Maxwell fields), represent a fundamental physics effect, and are not related to eddy currents or imperfection in hardware design and manufacture. Although Maxwell terms have been known for at least a decade, their effect on imaging has been largely ignored because of their negligible effect under conventional imaging conditions.
In axial echo planar imaging (EPI) carried out in a horizontal field magnet, it has been observed that the image in an off-center slice (z.noteq.0) can shift along the phase-encoded direction. The amount of the shift (.DELTA.y) is proportional to the square of the slice location z (.DELTA.y.varies.z.sup.2). This parabolic shift can cause image misregistration problems in neuro-functional imaging, where activation maps obtained from EPI images are overlaid onto a high resolution non-EPI image to establish the correlation between brain function and anatomy. Even in non-functional imaging, the shift can confuse clinical diagnosis and therapeutic planning, especially when the axial 2D slices are reformatted into arbitrary planes. Clearly, the source of this shift needs to be identified, and methods to remove the shift need to be developed.